“He’s moved into her life – and a little too easily, too,” the source tells PEOPLE. “I think her family is watching him closely.”

Lopez’s possible cold front comes amid tabloid reports about Smart: One claims he visited a New York City exotic massage parlor, while another reports he was at a peep show next door. (Photographs show Smart going up a set of stairs that lead to the spa.) Lawyers for the couple call the stories “false, malicious and defamatory.”

Those rumors coincided with her 43rd birthday, which they celebrated together in the city. But although they were all smiles as they were photographed heading to lunch, the source says “she’s getting frustrated with him” and she’s increasingly “short-tempered when she’s around him.”

This is a departure from the affection they displayed when they hit the town – and, recently, in a steamy music video for her single “Dance Again” (and again in a sweet clip during her current concerts for the song “Baby I Love U”).

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